%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  2-dimensionale Trapezregel
%  
% Integrationsgebiet Rechteck im R^2
%
close all                      
clear all 

n=600;
xmin=0;xmax=1;ymin=0;ymax=1; % Rechteckgrenzen
hx=(xmax-xmin)/n;
hy=(ymax-ymin)/n;

xi=[xmin:hx:xmax];
yj=[ymin:hy:ymax];
[X,Y]=meshgrid(xi,yj);
F=Normalxy(X,Y);
Integral=sum(sum(F(2:n,2:n),1),2); % Alle inneren Punkte mit Gewicht 1
Integral=Integral+1/2*(sum(F(1,2:n),2)+sum(F(n+1,2:n),2)...
         +sum(F(2:n,1),1)+sum(F(2:n,n+1),1));
Integral=Integral+1/4*(F(1,1)+F(1<n+1)+F(n+1,1)+F(n+1,n+1));
Integral=Integral*hx*hy;

fprintf('%s%30.16f \n',' Integralwert: ',Integral)